We have investigated the dephasing processes in a weak localization (WL) experiment of a two-dimensional electron system on liquid helium. From low-field magnetoconductivity measurements we can separate the damping of WL on the dephasing of electrons due to electron-electron interaction and the motion of the helium vapour atoms. We observe an intermediate regime where both damping mechanisms are of comparable importance and determine the cross-over from one dominant regime to the other.